A190153 Row sums of the triangle A190152.

1, 2, 12, 65, 351, 1897, 10252, 55405, 299426, 1618192, 8745217, 47261895, 255418101, 1380359512, 7459895657, 40315615410, 217878227876, 1177482265857, 6363483400447, 34390259761825, 185855747875876, 1004422742303477, 5428215467030962

Offset

0,2

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (5,2,1).

Formula

a(n) = Sum_{k=0..n} binomial(3*n-k,3*n-3*k).

From Colin Barker, Mar 21 2012: (Start)

a(n) = 5*a(n-1) + 2*a(n-2) + a(n-3).

G.f.: (1-3*x)/(1-5*x-2*x^2-x^3). (End)

Maple

seq(add(binomial(3*n-k, 3*n-3*k), k=0..n), n=0..20);

Mathematica

Table[Sum[Binomial[3n - k, 3n - 3k], {k, 0, n}], {n, 0, 22}]
LinearRecurrence[{5, 2, 1}, {1, 2, 12}, 30] (* G. C. Greubel, Dec 30 2017 *)

Prog

(Maxima) makelist(sum(binomial(3*n-k, 3*n-3*k), k, 0, n), n, 0, 22);
(PARI) x='x+O('x^30); Vec((1-3*x)/(1-5*x-2*x^2-x^3)) \\ G. C. Greubel, Dec 30 2017
(Magma) I:=[1, 2, 12]; [n le 3 select I[n] else 5*Self(n-1) +2*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Dec 30 2017

Crossrefs

Cf. A190152, A190154.

Sequence in context: A345697 A097632 A076804 * A372369 A369111 A334772

Adjacent sequences: A190150 A190151 A190152 * A190154 A190155 A190156

Keyword

nonn,easy

Author

Emanuele Munarini, May 05 2011

Status

approved